As has been stated, this is part of the game. Their actual feelings toward Feds may not actually be reflected in their rhetoric. I don't like that it works that way, but it does. So the question that begs is why is this the rhetoric? Because they perceive it as what they're constituencies want to hear.
What do we do about that? Provide damn good service and solutions where they're needed most. I have to (perhaps self-indulgently) tip my hat here to our Congressional Affairs Team at the USGS. They have done a wonderful job of working with our scientists to show members of Congress exactly how the USGS serves not just the nation but those Members' respective constituencies right where they live. They bring them solutions to problems, not problems themselves. And of the Members who are familiar with us (especially in our Approps Committee), they really like us, on both sides of the aisle.
Long pontificating short: Give citizens what they need, where they need it; do the same for Congress -- makes it a lot harder to gripe.